Question

Find the equations of the planes that passes through three points (1, 1, – 1), (6, 4, – 5),(– 4, – 2, 3)

Options

• `a/0 = b/0 = c/0`

• `a = b = c`

• `2a + b + c` = 0

• `3a + 2b + c` = 0

Answer 1

`a/0 = b/0 = c/0`

Explanation:

The planes passes through the points.

(1, 1, – 1), (6, 4, – 5),(– 4, – 2, 3)

Let the equation of plane passing through (1, 1, –1) be

`a(x - 1) + b(y - 1) + c(z + 1)` = 0  ......(1)

(6, 4, – 5) lies on it

∴ `a(6 - 1) + b(4 - 1) + c(-5 + 1)` = 0

or `5a + 3b - 4c` = 0  ......(ii)

(– 4, – 2, 3) lies on the plane

∴ `a(-4 - 1) + b(-2 - 1) + c(3 + 1)` = 0

or `-5a - 3b + 4c` = 0  ......(iii)

or `5a + 3b - 4c` = 0

From (2) and (3)

`a/(-12 + 12) = b/(-20 + 20) = c/(15 - 15)` or `a/0 = b/0 = c/0`

There is no way to draw a single plane.